For a narrow band of values of the top quark and Higgs boson masses, the Standard Model Higgs potential can develop a false minimum at energies of about 10^15-10^16 GeV, where primordial Inflation could have happened. I will present two mechanisms to achieve a successful transition from Inflation to a radiation dominated era: by adding a Brans-Dicke scalar to gravity or by introducing a hybrid model with a new scalar very weakly coupled to the Higgs. This has been predicted to happen only for a narrow window of values for the Higgs mass, of about (126 +- 3) GeV, which has been confirmed by the Higgs boson discovery at 125 GeV. We discuss the features of the models and point out that they can be further checked with: more precise measurements of the top quark mass and by cosmological observables (especially the tensor-to-scalar ratio).